A method of digital in-flight computation based on binary-coded encoding

Abstract

The application discloses a digital air computing method based on binary complement coding, comprising the following steps: linear scaling and down rounding quantization are performed on a continuous analog signal to be calculated at a distributed device end, and the quantized value is converted into a binary complement sequence with a fixed length; a decoder is designed at a base station end based on a superposition result of each binary bit; each bit of the binary complement sequence is subjected to binary phase shift keying (BPSK) modulation, a frequency band is divided into a plurality of subcarriers by using orthogonal frequency division multiplexing (OFDM) technology, and a plurality of devices superimpose transmission on the same subcarrier for the same binary bit; equal power allocation is performed according to the weight priority of the binary bit, a transmission signal is preprocessed based on channel state information by using a truncated channel inversion strategy; a linear minimum mean square error (LMMSE) detector is applied to each subcarrier received signal at the base station end to estimate a superposition result; a multi-subcarrier mean square error minimization problem is constructed, and a greedy algorithm is used to optimize an active device set and a transmission power factor; and the application significantly improves the real-time performance and reliability of multi-device cooperative computing in actual application.

Description

Technical Field

[0001] This invention relates to the field of general computing coupling technology, specifically to a digital aerial computing method based on binary two's complement encoding. Background Technology

[0002] Next-generation wireless communication networks need to deeply integrate distributed computing capabilities to support the large-scale deployment of edge intelligent applications. Against this backdrop, AirComp technology has attracted much attention due to its communication-computing fusion characteristics. This technology utilizes the signal superposition characteristics of multiple access channels to directly perform distributed data aggregation and computation at the air interface, which can greatly improve spectrum efficiency and reduce end-to-end latency compared to traditional time-division transmission schemes.

[0003] However, the traditional AirComp implementation based on analog signal processing has significant limitations. First, its reliance on continuous amplitude modulation conflicts with the discrete symbol transmission mechanism of modern digital communication systems, requiring additional mixed-signal front-end configurations and increasing hardware costs. Second, the vulnerability of analog signals in fading channels results in larger computational errors compared to digital systems, hindering applications in high-reliability scenarios such as the Industrial Internet of Things (IIoT). Therefore, research into the fusion architecture of digital signals and AirComp has become a hot topic in recent years, with the core challenge being the establishment of a deterministic mapping relationship between superimposed discrete symbols and the target computation result.

[0004] Existing technologies mainly explore two directions: signal space partitioning-based methods achieve numerical mapping by designing special modulation constellation diagrams, and coding-based techniques simplify detection through numerical-symbol sequence conversion. However, the imbalance between complexity and efficiency severely restricts the practical deployment of digital AirComp. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a digital air computing method based on binary two's complement encoding to solve the technical problem of achieving joint optimization of power and device selection under dynamic channel conditions of large-scale distributed Internet of Things devices.

[0006] Technical solution: The present invention provides a digital aerial computation method based on binary two's complement encoding, comprising the following steps:

[0007] S1: At the distributed device end, the continuous analog signal to be computed is linearly scaled and quantized down to convert the quantized value into a fixed-length binary two's complement sequence; at the base station end, a decoder is designed based on the superposition result of each binary bit.

[0008] S2: Perform binary amplitude keying (BASK) modulation on each bit of the binary two's complement sequence, and use orthogonal frequency division multiplexing (OFDM) technology to divide the frequency band into multiple subcarriers, so that the same binary bit of multiple devices can be superimposed and transmitted on the same subcarrier.

[0009] S3: Power is allocated proportionally according to the weight and priority of binary bits, and the transmitted signal is preprocessed based on the channel state information using a truncated channel inversion strategy;

[0010] S4: At the base station, a linear minimum mean square error (LMMSE) detector is applied to estimate the superposition result of the received signals of each subcarrier;

[0011] S5: Construct a multi-subcarrier mean square error minimization problem, and optimize the activation device set and transmit power factor through a greedy algorithm.

[0012] Furthermore, step S1 specifically includes: using a quantizer Device data g k Quantified as

[0013]

[0014] in g max It is the maximum absolute value of the elements in the device data set; convert the decimal quantized value into an L-bit binary sequence including the sign bit, and then into a two's complement sequence {x}. k,1 ,x k,2 ,…,x k,L}, which is then used as the encoded output; the base station decoding rule is:

[0015]

[0016] in,

[0017] Furthermore, in step S2, each binary bit x k,l Modulated by BPSK:

[0018] s k,l =2x k,l -1

[0019] Using OFDM to store L symbols s k,l The signal is assigned to different subcarriers for transmission, and the formula for the received signal is as follows:

[0020]

[0021] Where, ρ k,l This represents the preprocessing factor of device k on subcarrier l. This indicates that the channel coefficients between device k and the base station follow a complex Gaussian distribution. Indicates power as Additive complex Gaussian noise.

[0022] Furthermore, in step S3, the preprocessing factor is defined as:

[0023]

[0024] in, The set of active devices selected for the l-th subcarrier segment, p l To ensure that the amplitude factor satisfies:

[0025]

[0026] Among them, P k,l This represents the transmit power budget allocated by device k on subcarrier l; P k,max This represents the total transmit power budget for device k. Power allocation follows:

[0027]

[0028] in It is a proportionality constant.

[0029] Furthermore, in step S4, based on the received signal y l The real part of the aggregation result r l Perform LMMSE detection and estimate the value. Where λ l and μ l These are the multiplicative and additive parameters for correcting the received aggregated signal, respectively. Represents the real part of a complex number;

[0030] The optimal parameters are:

[0031]

[0032]

[0033] Furthermore, in step S5, the optimization problem is solved for each subcarrier:

[0034]

[0035] The optimal set of activation devices is determined using a greedy algorithm. Calculate the corresponding optimal power factor

[0036] in,

[0037]

[0038] Furthermore, the specific implementation of the greedy algorithm includes: sorting the channel gains of each subcarrier device in descending order, traversing the active device configuration, and calculating the corresponding e. lAfter selecting the value, choose the device activation strategy corresponding to the minimum value.

[0039] Furthermore, the OFDM modulation process includes: performing IFFT transformation and adding a cyclic prefix after converting the BPSK symbols from serial to parallel at the transmitting end; and recovering the subcarrier signal by FFT after removing the cyclic prefix at the receiving end.

[0040] The present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the methods described herein.

[0041] An electronic device according to the present invention includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement any of the methods described herein.

[0042] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: This invention achieves over-the-air computing based on digital modulation by jointly designing the encoding / decoding and air interface aggregation processes. Its core advantages include: First, it proposes an equal-ratio power allocation strategy based on two's complement weights, prioritizing the reliability of high-bit data transmission and significantly improving the robustness of over-the-air computing under low signal-to-noise ratio conditions; Second, it designs a channel truncation and inversion preprocessing method to determine the optimal set of activated devices, effectively balancing computational accuracy and energy consumption in large-scale node scenarios; Third, it designs an optimal linear detection architecture, effectively reducing detection complexity. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2 This is a graph showing the normalized mean square error of the present invention and its variation with the signal-to-noise ratio. Detailed Implementation

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0046] like Figure 1 As shown, this embodiment of the invention provides a digital air computation method based on binary two's complement encoding, including the following steps:

[0047] Step S1: At the distributed device, the continuous analog signal to be calculated is linearly scaled and quantized into integer values ​​using a floor function. Then, the decimal quantized value is converted into a fixed-length binary sequence and then into two's complement form. At the base station, a decoder is designed based on the superposition of different bits of the two's complement sequence to ensure correct calculation results.

[0048] An over-the-air computing system consisting of one base station and K edge devices, where each edge device has a non-independent and identically distributed data source g.k The base station target aims to calculate the sum of all data, that is... To transmit the over-the-air aggregated digital signal, a down quantizer with b quantization bits is required. The continuous value g k Quantize it into a discrete quantity, and set g k The quantized version is represented as f enc (·) is defined as an encoding function, which further quantizes the values. The data is encoded into a two's complement sequence with L binary elements, and the data from multiple distributed devices are independently superimposed bit by bit. Finally, the superimposed result is decoded to reconstruct the target value. |·| represents rounding down, and |·| represents the absolute value.

[0049] Specifically, quantizer Device data g k Quantified as

[0050]

[0051] in g max It is the maximum absolute value of the elements in the device data set; convert the decimal quantized value into an L-bit binary sequence including the sign bit, and then into a two's complement sequence {x}. k,1 ,x k,2 ,…,x k,L}, which is then used as the encoded output; the base station decoding rule is:

[0052]

[0053] in, Based on the above encoding and decoding measures, in the absence of additional errors... satisfy:

[0054]

[0055] It can perform error-free calculations on discrete values.

[0056] Step S2: For each bit of the binary sequence, binary phase shift keying (BPSK) is used for digital modulation. Orthogonal frequency division multiplexing (OFDM) modulation is used to divide the available frequency band into multiple subcarriers, and the modulated symbol sequence is converted from serial to parallel, thus enabling parallel transmission on multiple subcarriers. Multiple distributed devices share the same frequency band, and digital symbols of the same bit are superimposed on the same subcarrier.

[0057] For transmission, BPSK modulation is used to modulate the aforementioned binary symbols into digital symbols. Multiple distributed devices share the same frequency band, and digital symbols with the same bit position need to be independently superimposed. Therefore, OFDM modulation is used, dividing the available frequency band into L subcarriers to support the parallel superposition of L symbols. The process is as follows: First, the modulated symbol sequence is converted from serial to parallel; then, at the transmitting end, based on the received signal, an IFFT transform is applied and a cyclic prefix (CP) is added, thus enabling parallel transmission on the L subcarriers; finally, the base station removes the CP and applies an FFT transform to obtain the superposition result.

[0058] Specifically, the BPSK modulation symbol is:

[0059] s k,l =2x k,l -1

[0060] Using OFDM to store L symbols s k,l The signal is assigned to different subcarriers for transmission, and the formula for the received signal is as follows:

[0061]

[0062] Where, ρ k,l This represents the preprocessing factor of device k on subcarrier l. This indicates that the channel coefficients between device k and the base station follow a complex Gaussian distribution. Indicates power as Additive complex Gaussian noise.

[0063] Step S3: Due to the fading effect of the wireless channel, on each subcarrier, a truncated channel inversion strategy is adopted to preprocess the transmitted signal based on the channel state information. Furthermore, based on the weights and priorities of different bits, an equal-ratio power allocation strategy is used to distribute the limited transmit power to each subcarrier.

[0064] Specifically, due to equipment power limitations, only a subset of equipment can be selected for inverse channel pre-inversion, ρ k,l The preprocessing factor for device k on subcarrier l is defined as follows:

[0065]

[0066] in, The set of active devices selected for the l-th subcarrier segment, p l To ensure that the amplitude factor satisfies:

[0067]

[0068] Among them, P k,l This represents the transmit power budget allocated by device k on subcarrier l; Pk,max This represents the total transmit power budget for device k. Power allocation follows:

[0069]

[0070] Where ω≥1 is a proportionality constant.

[0071] Step S4: On each subcarrier, the base station detects the actual superposition result using a linear minimum mean square error detector based on the received superposition signal.

[0072] Specifically, without loss of generality, we assume that the information source g k It is uniformly and symmetrically distributed. Based on the quantizer under consideration, the quantized code value x for each device can be inferred. k,l Follows the standard Bernoulli distribution Thus, the prior information for obtaining the ideal reception result satisfies:

[0073]

[0074] Since only some devices are activated, the actual received value is:

[0075]

[0076] in

[0077] Considering only the real-valued part, the aggregated result y l After passing through a linear minimum mean square error (LMMSE) detector, we obtain:

[0078]

[0079] Where λ l and μ l These are the multiplicative and additive parameters for correcting the received aggregated signal, respectively. Representing the real part of the complex number, the optimal modified multiplicative and additive parameters are as follows:

[0080]

[0081] Step S5: Construct the mean square error (MSE) minimization problem for multiple subcarriers. Based on the greedy search algorithm, determine the optimal device activation strategy and preprocessing scaling factor to further improve the calculation accuracy.

[0082] The problem of minimizing the MSE of multiple subcarriers needs to be constructed. Based on the greedy search algorithm, the optimal device activation strategy and preprocessing scaling factor are determined to further improve the calculation accuracy.

[0083] Specifically, substituting the optimal λ l and μl The minimum implementable MSE is represented as follows:

[0084]

[0085] Mean square error depends on uniform amplitude factor p l and equipment collection selection The settings can be further optimized to improve performance; specifically, the joint optimization problem on subcarrier l is expressed as:

[0086]

[0087] With p l The increase of e l Monotonically decreasing; therefore, for any given The optimal scaling factor is equal to:

[0088]

[0089] along with Increase, p l The number of devices to be activated decreases, and the two are negatively correlated. Therefore, only K traversals are needed to obtain the optimal number of activated devices. The specific process is as follows: First, set the channel attenuation modulus |h of the K devices. k,l Sort in descending order and number them. Next, calculate each |h k,l |Corresponding scaling factor p l Then, channel noise p l and the corresponding Substitute into e l In the process, the minimum MSE is calculated to obtain the optimal activation device. and the corresponding optimal scaling factor Finally, the results and corresponding The instructions are transmitted to the transmitter to guide the implementation of the plan.

[0090] like Figure 1As shown, the main process of this invention is as follows: First, the continuous analog signal to be calculated is linearly scaled, quantized and encoded into a fixed-length binary two's complement sequence, and a decoder is designed at the base station to ensure that the superimposed values ​​of different bits can obtain the correct calculation results; Second, each bit of the binary two's complement sequence is digitally modulated using a two-level phase shift keying method, and the available frequency band is divided into multiple subcarriers. OFDM modulation is used to enable multiple devices to transmit digital symbols with the same bits superimposed on the same subcarrier; Next, the transmit power is allocated according to the weight of different bits using an equal power allocation strategy, and the signal is preprocessed using a truncated channel inversion strategy based on channel state information; Then, the linear detection parameters are derived based on prior information to minimize the mean square error; Finally, the optimal set of active devices for each subcarrier is quickly selected using a heuristic algorithm, and the calculation results guide the preprocessing operation at the transmitting end.

[0091] To verify the effectiveness of the present invention, a simulation experiment was conducted. The parameters involved in the simulation experiment are shown in the table below:

[0092] Table 1 Simulation Experiment Parameters

[0093] parameter Value Number of base stations 1 Number of users 20 Encoding bits 8 Number of sub-bands 8 Source Uniform distribution with variance of 1 Device power limit 0dBm

[0094] like Figure 2 As shown, the optimized encoding and decoding design algorithm proposed in this invention can effectively reduce the bit error rate under limited device transmit power conditions, and has a significant performance improvement compared with traditional analog and uniform power allocation schemes.

Claims

1. A method of binary-coded decimal over-the-air computation, comprising: The method comprises the following steps: S1: linearly scaling and down-integer quantizing the continuous analog signal to be calculated at the distributed device end, and converting the quantized value into a fixed-length binary sequence; At the base station end, a decoder is designed based on the superposition result of each binary bit; the preprocessing factor is defined as: wherein is the selected set of active devices in the 1th subcarrier, p l is the uniform amplitude factor satisfying: where P k,l denotes the transmit power budget allocated by device k on subcarrier l; P k,max denotes the total transmit power budget of device k; the power allocation follows: wherein is a proportionality constant; S2: binary phase shift keying (BPSK) modulation is performed on each bit of the binary complementary sequence, orthogonal frequency division multiplexing (OFDM) technology is used to divide the frequency band into multiple subcarriers, and multiple devices superimpose transmission of the same binary bit on the same subcarrier; each binary bit x k,l Through BPSK modulation: s k,l = 2x k,l -1 L symbols s k,l are allocated to different subcarriers for transmission using OFDM. The received signal is given by where ρ k,l denotes the pre-processing factor of device k on subcarrier l, denotes that the channel coefficients between device k and the base station obey a complex Gaussian distribution, denotes an additive complex Gaussian noise with power . S3: performing equal-power allocation according to the priority of the weight of the binary bit, and preprocessing the transmitting signal by using the truncated channel inversion strategy based on the channel state information; the preprocessing factor is defined as: wherein is the selected set of active devices in the 1th subcarrier, p l is the uniform amplitude factor satisfying: where P k,l denotes the transmit power budget allocated by device k on subcarrier l; P k,max denotes the total transmit power budget of device k; the power allocation follows: wherein is a proportionality constant; S4: applying a linear minimum mean square error (LMMSE) detector to each subcarrier received signal to estimate the superposition result; performing LMMSE detection on the aggregate result r l based on the real part of the received signal y l , and estimating value where λ l and μ l are the modified multiplicative and additive parameters for the received aggregate signal, respectively, representing the real part of a complex number; The optimal parameters are: S5: constructing a multi-subcarrier minimum mean square error minimization problem, and optimizing the active device set and the transmitting power factor by using a greedy algorithm; for each subcarrier, the optimization problem is solved: Determining an optimal set of active devices by a greedy algorithm Computing a corresponding optimal power factor wherein, 2. The method of claim 1, wherein the binary coded decimal is represented as a two's complement number. The greedy algorithm includes: arranging the sub-carrier device channel gains in descending order, traversing the active device configuration, calculating the corresponding e l value, and selecting the device activation strategy corresponding to the minimum value.

3. The digital aerial computation method based on binary two's complement encoding according to claim 1, characterized in that, The OFDM modulation process comprises: performing IFFT transformation and adding a cyclic prefix after performing serial-parallel conversion on the BPSK symbol at the transmitting end; and recovering the subcarrier signal by using FFT after removing the cyclic prefix at the receiving end.

4. A computer-readable storage medium, characterized in that, The computer program is stored in the memory and is executed by the processor to implement the method of any one of claims 1-3.

5. An electronic device, comprising: The computer program is stored in the memory and is executed by the processor to implement the method of any one of claims 1-3.

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